Finite Group Databasebeta

← Prev (#50304339) Next (#50304341) →

C3×C5×C7×C7⋊#261 #50304340

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C7×C7⋊#261

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C4
derivedC7×C13 ⋊ C3×C4×C5×C7
HallC5×C72×C13 ⋊ C3×C4
HallC3×C72×C13 ⋊ C4×C5
HallC3×C5×C72 ⋊ #261
HallC72×C13 ⋊ C3×C4×C5
HallC5×C72 ⋊ C3×#261
HallC3×C5×C13 ⋊ C7×Dic7
HallC3×C72 ⋊ C5×#261
HallC5×C13 ⋊ C3×C7×Dic7
SylowC72 ⋊ C3×C5×#261
HallC3×C13 ⋊ C5×C7×Dic7
SylowC13 ⋊ C3×C5×C7×Dic7

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7C7⋊#261
commutator, hypocenterC7×C13C3×C4×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C13C4
prime radicalC3×C5×C72×D13C2
cosocleC7×D13C2×C3×C5×C7
LCSG ▷ C7×C13
UCSC1 ◁ C3×C5×C7

144 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

3255 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1026);